What is the integral of tan(2x)sec^2(2x) ?

The integral of tan(2x)sec^2(2x) is 1/4 tan^2(2x)+C

Popular >

integral of tan(2x)sec^2(2x)

\int tan (2 x) sec^{2} (2 x) d x

\frac{1}{4} tan^{2} (2 x) + C

Solution steps

\int tan (2 x) sec^{2} (2 x) d x

Apply u-substitution

: \int \frac{u}{2} d u

= \int \frac{u}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{1}{2} \cdot \frac{u ^{2}}{2}

Substitute back

u = tan (2 x)

= \frac{1}{2} \cdot \frac{tan ^{2} ( 2 x )}{2}

Simplify

\frac{1}{2} \cdot \frac{tan ^{2} ( 2 x )}{2} : \frac{1}{4} tan^{2} (2 x)

= \frac{1}{4} tan^{2} (2 x)

Add a constant to the solution

= \frac{1}{4} tan^{2} (2 x) + C

\int \frac{e ^{t}}{e ^{2 t} + 3 e ^{t} + 2} d t

\int_{y}^{2} \frac{3}{16} x y d x

x^{2} + 21, at x = 2

x \to 1 lim (\frac{4 x - 4}{x - 1})

\int 16 x sin (x) d x

What is the integral of tan(2x)sec^2(2x) ?
The integral of tan(2x)sec^2(2x) is 1/4 tan^2(2x)+C